Aircraft: A300
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural MEL / CDL; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Fuel Issue; Inflight Event / Encounter Fuel Issue

Aircraft was dispatched with the RT INNER fuel quantity indicating system inop. Per the MEL; the RT INNER fuel tank quantity would have to be verified by an alternate means. Arrived at the aircraft; fueling was complete and the fuel service form had been signed but the alternate verification had not been recorded in the system. Called Maintenance and they said it was in progress and would be signed off shortly. First Officer (FO) confirmed that they were dripping the tank while he was on his pre-flight walk around.Received an ACARS alert that the system had changed; verified the MEL signoff and it confirmed 6;600 pounds in the right inner verified by Magnetic Level Indicator 2.Fuel Service form showed block in fuel of 19.2 lbs. and that 11.0 lbs. of fuel had been added to bring us up to a total 30.2 lbs.Climbing out of ZZZ got RT INNER FUEL tank pump fault. As Pilot Monitoring (PM) complied with ECAM and turned the pump off and consulted the QRH. When I brought the FUEL page back onto the ECAM I noticed the RT OUTER tank was burning and we had a fuel split of 1000 lbs between the RT and LT outer tanks. The working pump in the right inner tank showed a green line which I took to mean fuel pressure from the RT inner tank but the RT outer was burning down.I put the crossfeed valve in line so that LT inner tank was feeding the #2 Engine. Fuel stopped burning from the RT outer tank at that time. After a minute or two closed the crossfeed valve to see if the RT inner tank would now burn. Fuel started burning out of the RT outer again. Put crossfeed back in line to manually manage the fuel burn and to minimize the imbalance between outer tanks.FO and I discussed what we thought was going on. At this point I believed there was no fuel in the RT inner tank. We both agreed that we could not continue on to ZZZ1 and talked of possible diverts. We discussed returning to ZZZ but I believed there was no fuel in the RT outer tank and if that was the case; we already had an almost 7000 lb split between left and right sides.At this point we were about 50 miles to the west ZZZ2 and decided that was our best divert option. FO continued flying and worked with ATC to change destination and begin descending. I tried to contact ZZZ2 Ramp on VHF 2 but got no response. Informed operations via ACARS of a fuel discrepancy and that we were diverting to ZZZ2. He acknowledged and sent us routing and new numbers. Coordinated arrival with ZZZ Center and ZZZ2 Approach and shot a visual approach and landing to RWY XXR ZZZ2. Left inner tank was empty by the time we started the approach and were burning tank to engine on both engines.Once in the chocks we discussed what had happened and ran numbers on how much fuel we should have and how much we actually had. We blocked out with 29.2 and as per the fuel burn indicators had burned just a little over 10;000 lbs. We should have had 19;200 lbs. RT inner tank; inop FQIS; showed 5;900 lbs; but was empty. LT outer showed 7.4 and RT outer showed 6.0 for a total for a total of 13.4.ZZZ2 Maintenance verified fuel on board with MIL sticks. LT outer 7.7; LT inner 0.0; RT inner 0.0; RT outer 6.0 for a total of 13.7.A failure in the system ensuring required fuel is on board when dealing with a Fuel System MEL. Aircraft assigned had MEL for RT Inner fuel tank quantity indicator inoperative. When we got to aircraft and I began my walk around; I noticed maintenance moving a ladder over to the right wing inboard of the engine. As I got around to pre-flight the right main gear I asked the maintainer if they were checking the fuel quantity and he confirmed they were. This struck me as a bit odd since the system indicated Flight Ready when we were in ops. I finished my pre-flight and when I got to the cockpit I mentioned to the Captain they were checking the tank on pre-flight; but we both agreed there was no record of the check in the maintenance history. He called Maintenance and they said it was in work. We received an ACARS informing us the aircraft status changed to not flight ready. Shortly after we then received a Flight Ready ACARS notification. I then confirmed the fuel added from the previous flight block in and the fuel slip using the APS. The APS; fuel slip and fuel page all were within +/- 200-300 lbs of total quantity. We blocked out and departed on Runway XXR. After getting a turn east and a climb; ECAM indicated a RT Inner tank pump fault. The Captain began handling ECAM and QRH as Pilot Monitoring (PM). As Pilot Flying (PF); I was not head's down much but I did notice we had approximately a thousand pound split between the LT and RT outer tanks. The fuel page also showed the left pump in the RT inner tank still operational with a green line leading to the right engine. The RT inner showed approximately 5.7. The Captain informed me he was going to place the cross feed valve in-line to feed the right engine from left inner tank. When he did that the RT outer tank burn stopped. After a few minutes he closed the cross feed and again the RT outer tank quantity began decreasing after monitoring it for a minute or two. We then paced the valve back inline to manage imbalance. At this point we were leveling off and we began discussing what was taking place in the fuel system. Despite what the fuel system was indicating; we both came to the conclusion that there was no fuel remaining in RT Inner tank. Based on where we were; and the headwind we would have turning around to ZZZ; we elected to inform Center that we needed to land at ZZZ2. As PF; I took over ATC comms and FMS management to get a descent and set up for approach to ZZZ2 while the Captain attempted contacting operations via ACARS to tell them our situation and plan as well as call ZZZ2 Ramp. We descended and landed at ZZZ2 uneventfully. Once we were blocked in we discussed what we blocked out with-29.2 and had burned-10.0 per the fuel consumption gauges for each engine. The aircraft showed we had 19.2 onboard. We discussed this with Maintenance and they did the manual verification of the tanks confirming that the left and right inner tanks were empty and the actual fuel onboard was 13.7.Unsure other than a discrepancy between what amount of fuel was added and what reading was taken to manually verify RT inner tank quantity.I do not know what took place during the fueling / manual verification timeline to offer feedback on how to prevent future occurrences A300 flight crew reported MEL procedures were not followed correctly and they had to divert due to insufficient fuel loaded for the flight.